Turkish Journal of Mathematics
Abstract
For two finite monoids $S$ and $T$, we prove that the second integral homology of the Sch\"{u}tzenberger product $S\Diamond T$ is equal to $$H_{2}(S\Diamond T)=H_{2}(S)\times H_{2}(T)\times (H_{1}(S)\otimes _{\mathbb Z} H_{1}(T)) $$ as the second integral homology of the direct product of two monoids. Moreover, we show that $S\Diamond T$ is inefficient if there is no left or right invertible element in both $S$ and $T$.
DOI
10.3906/mat-1503-79
Keywords
Monoid, Sch\"{u}tzenberger product, second integral homology, efficiency
First Page
763
Last Page
772
Recommended Citation
YAĞCI, M, BUGAY, L, & AYIK, H (2015). On the second homology of the Sch\"{u}tzenberger product of monoids. Turkish Journal of Mathematics 39 (5): 763-772. https://doi.org/10.3906/mat-1503-79
